nalgebra/src/geometry/unit_complex.rs

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use std::fmt;
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use approx::ApproxEq;
use num_complex::Complex;
use alga::general::Real;
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use core::{Unit, SquareMatrix, Vector1, Matrix3};
use core::dimension::U2;
use geometry::Rotation2;
/// A complex number with a norm equal to 1.
pub type UnitComplex<N> = Unit<Complex<N>>;
impl<N: Real> UnitComplex<N> {
/// The rotation angle in `]-pi; pi]` of this unit complex number.
#[inline]
pub fn angle(&self) -> N {
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self.im.atan2(self.re)
}
/// The rotation angle returned as a 1-dimensional vector.
#[inline]
pub fn scaled_axis(&self) -> Vector1<N> {
Vector1::new(self.angle())
}
/// The underlying complex number.
///
/// Same as `self.as_ref()`.
#[inline]
pub fn complex(&self) -> &Complex<N> {
self.as_ref()
}
/// Compute the conjugate of this unit complex number.
#[inline]
pub fn conjugate(&self) -> Self {
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UnitComplex::new_unchecked(self.conj())
}
/// Inverts this complex number if it is not zero.
#[inline]
pub fn inverse(&self) -> Self {
self.conjugate()
}
/// The rotation angle needed to make `self` and `other` coincide.
#[inline]
pub fn angle_to(&self, other: &Self) -> N {
let delta = self.rotation_to(other);
delta.angle()
}
/// The unit complex number needed to make `self` and `other` coincide.
///
/// The result is such that: `self.rotation_to(other) * self == other`.
#[inline]
pub fn rotation_to(&self, other: &Self) -> Self {
other / self
}
/// Compute in-place the conjugate of this unit complex number.
#[inline]
pub fn conjugate_mut(&mut self) {
let me = self.as_mut_unchecked();
me.im = -me.im;
}
/// Inverts in-place this unit complex number.
#[inline]
pub fn inverse_mut(&mut self) {
self.conjugate_mut()
}
/// Raise this unit complex number to a given floating power.
///
/// This returns the unit complex number that identifies a rotation angle equal to
/// `self.angle() × n`.
#[inline]
pub fn powf(&self, n: N) -> Self {
Self::from_angle(self.angle() * n)
}
/// Builds the rotation matrix corresponding to this unit complex number.
#[inline]
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pub fn to_rotation_matrix(&self) -> Rotation2<N> {
let r = self.re;
let i = self.im;
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Rotation2::from_matrix_unchecked(
SquareMatrix::<_, U2, _>::new(
r, -i,
i, r
)
)
}
/// Converts this unit complex number into its equivalent homogeneous transformation matrix.
#[inline]
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pub fn to_homogeneous(&self) -> Matrix3<N> {
self.to_rotation_matrix().to_homogeneous()
}
}
impl<N: Real + fmt::Display> fmt::Display for UnitComplex<N> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "UnitComplex angle: {}", self.angle())
}
}
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impl<N: Real> ApproxEq for UnitComplex<N> {
type Epsilon = N;
#[inline]
fn default_epsilon() -> Self::Epsilon {
N::default_epsilon()
}
#[inline]
fn default_max_relative() -> Self::Epsilon {
N::default_max_relative()
}
#[inline]
fn default_max_ulps() -> u32 {
N::default_max_ulps()
}
#[inline]
fn relative_eq(&self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon) -> bool {
self.re.relative_eq(&other.re, epsilon, max_relative) &&
self.im.relative_eq(&other.im, epsilon, max_relative)
}
#[inline]
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
self.re.ulps_eq(&other.re, epsilon, max_ulps) &&
self.im.ulps_eq(&other.im, epsilon, max_ulps)
}
}